- #1
Joseph Chikva
- 202
- 2
Abstract
The proposing Method unlike to using now others comprises in usage for plasma creation
and its further ignition the created in-situ halo-layer of high-energetic particles to the
puffed gas.
For realization of Method the following procedures should be performed consistently and
corresponding hardware should be included in toroidal fusion reactor:
In-situ creation of halo-layer:
orthogonally to equatorial plane of toroidal vacuum chamber to create generally
the time-dependent magnetic field (bending field) penetrating only its curvilinear
segments,
to apply axial (toroidal) magnetic field only in the regions located remotely from
injection points,
along the axis of toroidal vacuum chamber to inject 3 different kinds of pulse high
current particle beams (two ions’ – reacting components and one – electron’s)
with such a parity of particles’ kinetic energies allowing them the capability of
moving in a given bending magnetic field on a common equilibrium orbit (gyroradiuses
(rg=p/qB) of all 3 spices are equal) in such a manner that faster ion beam
passes through the moving at the same direction slower ion beam with sufficient
for nuclear fusion collision energy and the relativistic electron beam moving
oppositely to ions thus allowing to combined beam the self-focusing capability,
to apply axial (toroidal) accelerating electric field compensating the occurring
together with fusion two effects: tendency of alignment of velocities of reacting
particles and also electrons’ energy losses via Bremsstrahlung.
Number density up to 1024 m-3 and even higher is achievable in combined beam and as
result of fusion the high energetic fusion products are produced, from which neutrons
escape reactor while charged particles form halo-layer.
For creation of plasma and its ignition at once after injection:
from the walls with the help of corresponding valves to puff into the vacuum
chamber the gas consisting the fuel components. And already being there halolayer
ionizes that gas and then generates the current similarly to that how current
is driven by beam/beams of neutrals in modern TOKAMAKs.
in regions being free from axial magnetic field to apply such a field at once after
the end of injection.
The Method allows the reliable ignition of plasma in all kinds of toroidal fusion reactors.
Claims
1. The Method for creation of plasma and ignition of self-sufficient reaction intoroidal fusion reactors, the Method comprising the following procedures that
should be performed consistently and corresponding hardware should be included
in toroidal fusion reactor:
1. Orthogonally to equatorial plane of toroidal vacuum chamber to create
generally the time-dependent magnetic field (bending field) penetrating only
its curvilinear segments (as generally the toroidal chamber may also have
rectilinear segments – racetracks).
2. To apply axial (toroidal) magnetic field in the regions located remotely from
injection points
3. Along the axis of toroidal vacuum chamber to inject 3 (three) different kinds
of pulse high current particle beams (two ions’ – reacting components and one
– electron’s) with a such a parity of particles’ kinetic energies and
corresponding momentums (depending on particles’ mass-to-charge ratio)
allowing them the capability of moving in a given bending magnetic field on a
common equilibrium orbit in such a manner that faster ion beam passes
through the moving at the same direction slower ion beam with sufficient for
nuclear fusion collision energy and the relativistic electron beam moving
oppositely to ions thus allowing to combined beam the self-focusing (pinch)
capability thanks to the only partial compensation of reacting ions’ positive
space charge and also to the magnetic attraction of all 3 (three) unidirectional
currents creating self-magnetic field (poloidal field),
4. To apply axial (toroidal) accelerating electric field compensating the
occurring together with fusion two effects: tendency of alignment of velocities
of reacting particles and also energy losses of electrons via Bremsstrahlung.
(Similarly to how current driving field is induced e.g. in TOKAMAKs). For
preservation of comparatively constant value of equilibrium orbit’s radius the
action accelerating field should be coordinated with increase in intensity of
bending magnetic field. Such a requirement is automatically satisfied in
betatrons without any external regulation while in synchrotrons external
regulation is used. So, even in case of necessity of regulation that is
achievable and would not be a big problem.
5. To puff the gas consisting the fusion fuel components from the walls into the
vacuum chamber until filling of chamber to desired pressure. Halo-layer will
ionize the gas and then will generate the current similarly to that how current
is generated in so called Advanced TOKAMAKs (H-mode – beam driven
current)
6. At once after injection in regions free from axial magnetic field to apply such
a field similar to that is applied in TOKAMAK reactors
2. The procedure and corresponding hardware of claim 1, the bending magnetic
field directed orthogonally to equatorial plane of toroidal vacuum chamber
(vertically) penetrating only its curvilinear segments.
As a rule the vacuum chamber of toroidal fusion reactors has a round central axis
but generally round segments can alternate with the rectilinear segments
(racetracks). As the Method is proposing injection along the axis of high current
beams, presence of racetracks would be preferable as they provide easier
injection.
Such racetracks have been used in first Stellarators. Also they widely used in high
energy particle accelerators for example racetrack FFAG betatron for Muon
Fabric (Brookhaven National Laboratory) or Induction Synchrotron (All-ion
Accelerator) developing now by KEK (High Energy Accelerator Research
Organization)
And it is proposed to create orthogonally to equatorial plane of vacuum chamber
the bending magnetic field penetrating only its curvilinear segments. Such a field
may be created by dipole magnets like to how similar purpose fields are created in
synchrotrons or by betatron type magnet systems. The order of initial value of that
field would be 0.1-0.4T. Then in the course of acceleration field’s induction
should be increased correspondently to instant momentums of maintaining
particles, thus keeping comparatively constant equilibrium radius.
3. The procedure and corresponding hardware of claim 2, to apply axial (toroidal)
magnetic field only in the regions located remotely from injection points
Periodic axial magnetic field is needed for avoiding or slowing down of
instabilities (e.g. two-stream instability)
As it is shown in number of papers [e.g. 9], such a field dramatically expands
stability area.
At the injection moment beams injection points should be free from influence of
that field.
4. The procedure and corresponding hardware of claim 3, to inject into the
common axis (axis of vacuum chamber) 3 (three) pulse high current beams.
It is offered to inject two beams of particles of reacting components and to direct
them along the same orbit and at the same direction but with different coherent
motion velocities.
So, one faster ion beam should transit (pass) through another slower ion
beam and their relative velocity should be sufficient for providing to reacting
nuclei enough collision energy required for fusion (enough energy for
Coulomb barrier overcoming).
For achievement of sufficient intensity of nuclear fusion the focusing of reacting
beams is necessary. For this purpose it is offered to direct the relativistic electrons
beam along the same orbit but towards (oppositely) to reacting particles beams.
This relativistic electron beam should compensate the positive space charge
only partially and at the same time thanks to the magnetic attraction of
combined three beams (three unidirectional currents) will compress the whole
system in radial direction (pinch-effect). In fact pinch-effect will be provided
thanks to the circumstance that in frame of reference connected with ions
combined beam will charged negatively and for frame of reference connected
with electrons – positively.
In the first approximation (not taking into consideration self-fields and influence
of walls) the condition for beams for moving along the same equilibrium orbit is
equality of gyroradiuses of particles.
Gyroradius can be calculated by the formula:
rg=p/qB (1),
Where:
rg – gyroradius of particle
q – charge
B – induction of bending field
And equality of gyroradiuses for equally charged particles (e.g. deuterium, tritium
and electron) means that their coherent motion momentums should be equal.
And e.g. for:
Deuterium – 450keV
Tritium – 300keV
Electron – 40.6MeV
all momentums are equal to ~2.2*10-20 kg*m/s and at Bb=0.1T
rg=~1.4m
Deutrons 450keV and Tritons 300keV moving along the same axis at the same
direction have center-of-mass collision energy ~30keV.
Such an energy provides rather high fusion cross section equal to ~1barn
G.I.Budker [1] says about achievability of order of magnitude of number density
in such beams of 1026m-3 and even higher and beam’s radius of fractions of mm.
Generally radial dimension of combined beam is a function of circulating
currents, positive space charge neutralization level, coherent velocities of ions,
relativistic factor γe and temperature. And varying with electron current for a
given ion currents we can easily control the radius of combined beam.
For a given above sample of particles’ energies:
γe=80.5 (relativistic factor of electrons in fixed frame of reference)
γt=81.6 (relativistic factor of electrons in frame of reference connected with tritium)
γd=82.2 (relativistic factor of electrons in frame of reference connected with deuterium)
And if nd=nt=ni/2, condition of pinch (excess of magnetic attraction forces on
space charge repulse forces) will be:
ne>1/3355ni
So, the combined beam may be dramatically non-neutral and nevertheless
suffering pinching. And this circumstance would be salutary for energy balance.
Injection challenge
Injection into vacuum chamber of very high current beams is a challenge. As the
currents of thousands Amperes order for electron beam and tens/hundred
thousand Amperes for ions are required. And before neutralization such beams are
space charge dominated.
But induction electron accelerators (Induction Linacs) produce rather high quality
beams (energy spread <1%) and, so, having narrow phase volume (space), radius
of vacuum chamber would have 0.5-2m order, while electron beam’s radius
before injection – ~0.15m and electrons will be high relativistic 40.6MeV
(γe=80.5, repulse forces reduce by factor of 1/γ2).
And commonly the injection of intense relativistic electron beams is well
developed in number of laboratories [3] Fig. 1
And if we would inject firstly the electron beam and that then will totally fill the
whole circumference (along axis) of chamber, the rather deep potential well for
positively charged particles will be created, the depth of which is equal to [2]:
W=ve(1+2ln(R/Re)mec2 (2),
Where:
ve – Budker’s parameter ve = Ne2/m0c2 N-linear density (for Ie=4kA ve=0.235)
R – radius of vacuum chamber
Re – radius of electron beam
And for Ie=4kA, R=0.75m, Re=0.113m (je=10A/cm2)
W=1.123*mec2=574keV
And 574keV is rather enough depth for effective injecting into the same space
ions producing by ion diodes even despite the fact that they have high energy
spread and, so, big phase space.
Energies of ions:
Deuterium – 450keV
Tritium – 300keV
Injectors
For electron injection it is more suitable to use Induction Linear Accelerators
(Induction Linacs) producing:
currents of kilo-amperes orders (10000 A by ATA accelerator [7])
particles energies up to 50 MeV (with the spread <1% [7])
pulse duration – 50 ns -1.2 μs
These parameters allow the effective injection of electron beams into the chamber
with reasonable radial dimension (up to 2 m for modern TOKAMAKs)
For ions – the Ion Diodes or combination of Ion Diodes with additional Inductive
Voltage Adders would be more suitable.
As:
Ion Diodes produce currents up to mega-Amperes orders
Energies of particles – up to several MeV (several hundreds keV are more
common)
Pulse duration – 50 ns – several μs
But energy spread produced by Ion Diodes is rather high and, so, ion beams
occupy big phase space.
From the one side wide spread would be useful for avoiding of some types of
instabilities (e.g. two-stream instability) but from another – it makes more
difficulties for injections. But as has been showed above, if electron beam would
be injected before ions, that creates enough potential well for further injection of
ions. Combination of Ion Diodes with Inductive Voltage Adders also
dramatically reduces spread.
5. The procedure and corresponding hardware of claim 4, to apply the axial
(toroidal) accelerating electric field.
If considering elastic collision of two particles moving at the same direction with
different velocities, faster moving particle will transfer some momentum (and
corresponding energy) to slower one, thus accelerating that and decelerating itself.
For the case when slower particle has bigger mass [1], [4]:
ΔE=γ2β2mc2 Θ/2
(3)
Δp= ΔE/v,
Where:
γ – relativistic factor of faster particle in the frame connected with slower
β – vrelative/c (vrelative - relative velocity of two particles)
m – mass of faster particle
Θ – scattering angle
And for interesting for us case average energy loss of faster moving Deuteron per
each elastic collision (scattering event):
ΔE=10.9eV (corresponds to Θ=0.85 deg)
And taking into account that ratio between scattering and fusion cross sections
differs on about 4 orders of magnitude, we should wait that:
Deuteron 450keV decelerates to ~340keV
Triton 300keV accelerates to ~410keV
before they fuse.
Naturally, mentioned above kinetic energies do not provide collision energy
sufficient for fusion (not less than 10keV in center-of-mass frame)
And for this reason it is offered to apply along the axis the electric field
accelerating particles in a manner similar to TOKAMAK in which that firstly
breakdowns gas, ionizing that and drives the current.
TOKAMAK needs comparatively high intensity of electric field initially (up to
100 V/m when gas breakdown goes) but then by growth of plasma conductivity
required intensity should be much lower (typical value of loop voltage – from
fraction of Volt to 1 Volt which corresponds to 0.5V/m of intensity and even
lower). Nevertheless due to high conductivity of hot plasma this voltage drives
mega-Amperes order current.
For estimation of required intensity of electric field let us admit that:
number density of pinched combined beam – 1023 m-3
required confinement time in this case – 10-3 sec
And in this time the electric field of 50 V/m intensity will give to deuterium
additional energy ~387keV and to tritium – ~240keV
And as result after the lapse of offered cycle will have:
Deuteron 450keV accelerates to ~727keV
Triton 300keV accelerates to ~650keV
that provides collision energy in center-of-mass frame
21.6keV (quite sufficient for fusion)
Here we should also to notice that particles from the beginning having equal
gyroradiuses as result of described phenomena gain the certain mismatch from
equilibrium momentums (about 18%) but also we have described that attraction of
three unidirectional currents creates enough potential well confining them
together.
According data provided by Stallatron (high current Betatron with additional
Stellarator type windings) developers [5] such a scheme allows mismatch of
energies up to 50% from equilibrium.
Requirements on axial electric field
For creation of axial electric field if we would use iron core transformer made of
permendur (saturation limit 2.5 T), circumference of toroidal chamber L=15 m,
inner area available for core S=20 m2 , mentioned above electric field E=50 V/m
intensity can be kept in:
Bmin= - 2.4 T
Bmax= 2.4 T
Loop voltage :
Vloop=LE
t= S(Bmax-Bmin)/LE=0.128 sec = 128 milliseconds
So, after 1 millisecond there is enough reserve to pass then on lower intensity
(~0.5 V/m) using in TOKAMAK mode with hot plasma.
6. The procedure and corresponding hardware of claim 5, at once after injection
from the walls with the help of corresponding valves to puff into the vacuum
chamber the gas consisting the fusion fuel components until filling the
chamber up to desired pressure.
It is offered to use several gas-puff valves divided along circumference of reactor
in regular intervals and to open them at certain moment puffing the certain
quantity of gas: e.g. equal (by volume) mix of deuterium and tritium gases.
Already being there halo-layer will ionize that gas and then generate the current
similarly to that how current is generated in so called Advanced TOKAMAKs (Hmode
– beam driven current) and rise the temperature until thermonuclear
temperature (higher than 10keV)
As the energy of halo-layer is in more convenient for energy transfer form – fast
moving ions, energy of those ions 3.5MeV + energy corresponding to velocity of
center-of-mass frame (2.63*106 m/s in considering here case) and that energy will
be absorbed by cold gas within a few milliseconds increasing its temperature to
desired value (10 keV and higher)
7. The procedure and corresponding hardware of claim 6, at once after injection in
regions free from axial magnetic field to apply such a field similar to that is
applied in TOKAMAK reactors
Injection of charged particles across force lines of magnetic field is impossible.
So, initially there should not be an axial/toroidal magnetic field at least near
injection points.
But axial field is necessary for further confinement of hot plasma (that is the one
of the main components of TOKAMAK confinement concept)
And there are some methods of fast creation of axial fields and then keeping them
at constant value during certain period.
For example to use two coils: so called ―fast coil‖ being lower in diameter, having
lower inductance but conducting very high current. Such a coil may create short
pulse magnetic field, while larger but more inductive coil’s field will rise slower
but for longer time period till the end of necessity of confinement.